Question 752297: A polynomial functions f has x- intercepts at -5,-3,0,6? Which is a possible equation for the function?
A. f(x)=(x+5)(x+3)(x-6)
B. f(x)=x(x+5)(x+3)(x-6)
C. f(x)=(x-5)(x-3)(x+6)
D. f(x)=x(x-5)(x-3)(x+6)
I typed it up exactly how it is on the review. (This is not a question on a test, this is a question on the review for the test. SO I really need to know how to solve this)
Found 2 solutions by josgarithmetic, KMST:
Answer by josgarithmetic(39618)   (Show Source):
You can put this solution on YOUR website! Look at this logically. You have FOUR x-intercepts and you are looking at function choices composed of three or four binomial factors. Which choices can you eliminate? Which choices remain?
Now, intercept matching to factor, which choice works and which choice does not work?
These are what you choose from:
B. f(x)=x(x+5)(x+3)(x-6)
D. f(x)=x(x-5)(x-3)(x+6)
Examine each given intercept to see which function will be f(c)=0 for each value c of your given intercepts.
Answer by KMST(5328)  (Show Source):
You can put this solution on YOUR website! If the function has x- intercepts at -5, -3, 0, and 6, it means that f(x) is zero for those values of x.
As a consequence, when the function is factored, it must have all of the following factors:
(x-(-5))=(x+5), which becomes zero when x=-5,
(x-(-3))=(x+3), which becomes zero when x=-3,
(x-0)=x, which becomes zero when x=0, and
(x-6), which becomes zero when x=6.
(It could have other factors too, but it must have those four factors).
So  .  is the only option that works.
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